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The interaction between noise and transport mechanisms in PDEs. (English) Zbl 1231.35165

Summary: The understanding of transport mechanisms in PDEs is at the core of some of the main open problems in fluid dynamics. The introduction of random perturbations in these equations may have an influence on the properties of transport. We report here some recent progresses on the interaction between noise and transport. The Lagrangian viewpoint is used to investigate the problem. In some example we observe that noise improves the properties of the Lagrangian motion and restores uniqueness or prevents blow-up of the associated PDE; in other examples this does not happen.

MSC:

35Q35 PDEs in connection with fluid mechanics
35D30 Weak solutions to PDEs
35B44 Blow-up in context of PDEs
35R60 PDEs with randomness, stochastic partial differential equations
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